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Joint IAS/Princeton University Number Theory Seminar

Slopes in eigenvarieties for definite unitary groups

The study of eigenvarieties began with Coleman and Mazur, who constructed the first eigencurve, a rigid analytic space parametrizing $p$-adic modular Hecke eigenforms. Since then various authors have constructed eigenvarieties for automorphic forms on many other groups. We will give bounds on the eigenvalues of the $U_p$ Hecke operator appearing in Chenevier's eigenvarieties for definite unitary groups. These bounds generalize ones of Liu-Wan-Xiao for dimension $2$, which they used to prove a conjecture of Coleman-Mazur-Buzzard-Kilford in that setting, to all dimensions. We will then discuss the ideas of the proof, which goes through the classification of automorphic representations that are principal series at $p$, and a geometric consequence.

Featuring

Lynnelle Ye

Speaker Affiliation

Harvard University

Affiliation

Mathematics

Event Series

Video

https://video.ias.edu/puias/2018/1206-LynnelleYe
Date & Time
December 06, 2018 | 4:305:30pm

Location

Simonyi Hall 101

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